Incorporating biological prior knowledge for Bayesian learning via maximal knowledge-driven information priors

Abstract

BackgroundPhenotypic classification is problematic because small samples are ubiquitous; and, for these, use of prior knowledge is critical. If knowledge concerning the feature-label distribution – for instance, genetic pathways – is available, then it can be used in learning. Optimal Bayesian classification provides optimal classification under model uncertainty. It differs from classical Bayesian methods in which a classification model is assumed and prior distributions are placed on model parameters. With optimal Bayesian classification, uncertainty is treated directly on the feature-label distribution, which assures full utilization of prior knowledge and is guaranteed to outperform classical methods.ResultsThe salient problem confronting optimal Bayesian classification is prior construction. In this paper, we propose a new prior construction methodology based on a general framework of constraints in the form of conditional probability statements. We call this prior the maximal knowledge-driven information prior (MKDIP). The new constraint framework is more flexible than our previous methods as it naturally handles the potential inconsistency in archived regulatory relationships and conditioning can be augmented by other knowledge, such as population statistics. We also extend the application of prior construction to a multinomial mixture model when labels are unknown, which often occurs in practice. The performance of the proposed methods is examined on two important pathway families, the mammalian cell-cycle and a set of p53-related pathways, and also on a publicly available gene expression dataset of non-small cell lung cancer when combined with the existing prior knowledge on relevant signaling pathways.ConclusionThe new proposed general prior construction framework extends the prior construction methodology to a more flexible framework that results in better inference when proper prior knowledge exists. Moreover, the extension of optimal Bayesian classification to multinomial mixtures where data sets are both small and unlabeled, enables superior classifier design using small, unstructured data sets. We have demonstrated the effectiveness of our approach using pathway information and available knowledge of gene regulating functions; however, the underlying theory can be applied to a wide variety of knowledge types, and other applications when there are small samples.

Optimal Bayesian Transfer Learning

“…This has been studied under different conditions in the context of the OBC: using the data from unused features to infer a prior distribution [41], deriving the prior distribution from models of the datagenerating technology [35], and applying constraints based on prior knowledge to map the prior knowledge into a prior distribution via optimization [42], [43], [44]. The methods in [42], [43] are very general and have been placed into a formal mathematical structure in [44], where the prior results from an optimization involving the Kullback-Leibler (KL) divergence constrained by conditional probability statements characterizing physical knowledge, such as genetic pathways in genomic medicine. A key focus of our future work will be to extend this general framework to the OBTL, which will require a formulation that incorporates knowledge relating the source and target domains.…”

Autonomous efficient experiment design for materials discovery with Bayesian model averaging

“…The so-called Bayesian Optimization (BO) [12] in the literature corresponds to these cases, where the prior model is sequentially updated after each experiment. Bayesian parametric and nonparametric models are widely used in other fields such as bioinformatics [13][14][15][16][17][18]. When prior knowledge about the form of the objective function exists and/or many observations of the objective values at different parts of the input space are available, one can use a parametric model as a surrogate model.…”

Multivariate Calibration and Experimental Validation of a 3D Finite Element Thermal Model for Laser Powder Bed Fusion Metal Additive Manufacturing

“…Examples of constructing informative prior distributions using additional prior knowledge can be found in [66,67]. The lower and upper bounds for these prior distributions, (α θ i , β θ i ), were set equal to the lower and upper bounds of the parameters space T min = {20%, 40%, 1}, and T max = {70%, 90%, 25}.…”